Finite Group Databasebeta

← #21453855

Subgroups — #21453855

Order 7808.

444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519757C211yesmaximal, characteristic
2C2×#14519755C211yesmaximal, characteristic
3#16839704C212yesmaximal, complemented
4#16839700C211yesmaximal, characteristic, complemented
5#16839691C212yesmaximal
6#16839689C212yesmaximal
7#16839683C211yesmaximal, characteristic, complemented
8#16839683C212yesmaximal, complemented
9#16839682C211yesmaximal, characteristic, complemented
10#16839624C211yesmaximal, characteristic
11C61×#400C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×Dic122C2211yescharacteristic
14C22×C4×D61C2211yescharacteristic
15#14519757—24no—
16#14519755—24no—
17C2×C4⋊Dic61C2212yes—
18C2×C4⋊Dic61C2212yes—
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2212yes—
22C2×#11758198C2211yescharacteristic
23C2×#11758198C2212yes—
24C2×#11758198C2211yescharacteristic
25C2×#11758198C2212yes—
26#14519684C2212yes—
27#14519684C2211yescharacteristic
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34#95×C61C2212yes—
35#95×C61C2211yescharacteristic
36#95×C61C2212yes—
37C23×D61C2311yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C22×C4×C61C2312yes—
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2312yes—
42C22×C4×C61C2311yescharacteristic
43C22×Dic61C2311yescharacteristic
44C22×Dic61C2312yes—
45C22×Dic61C2312yes—
46C22×Dic61C2311yescharacteristic
47C22×Dic61C2311yescharacteristic
48C2×C4×D61—42no—
49C2×C4×D61D414yes—
50C2×Dic122—22no—
51C2×Dic122—22no—
52C2×Dic122—42no—
53C2×Dic122—42no—
54C4⋊C4×C61—22no—
55C4⋊C4×C61—22no—
56#11758198—22no—
57#11758198—22no—
58#11758198—24no—
59#11758198—42no—
60C4⋊Dic61—24no—
61C4⋊Dic61—42no—
62#11758196—22no—
63#11758196—22no—
64#11758196—42no—
65C23×C61C2411yescharacteristic
66C22×D61—22no—
67C22×D61—22no—
68C22×D61—21no—
69C22×D61—21no—
70C22×D61C2×D412yes—
71C2×C4×C61—22no—
72C2×C4×C61—21no—
73C2×C4×C61—22no—
74C2×C4×C61—21no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—21no—
78C2×C4×C61—24no—
79C2×C4×C61—21no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61C2×D412yes—
83C2×Dic61—22no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61C2×D412yes—
96C4×D61—44no—
97Dic122—44no—
98Dic122—44no—
99C22×C61C22×D411yescharacteristic
100C22×C61H(5,𝔽2)12yes—
101C22×C612−1+411yescharacteristic
102C22×C612−1+412yes—
103C22×C612−1+411yescharacteristic
104C2×D61—22no—
105C2×D61—22no—
106C2×D61—22no—
107C2×D61—42no—
108C2×D61—42no—
109C4×C61—22no—
110C4×C61—41no—
111C4×C61—42no—
112C4×C61—41no—
113C4×C61—42no—
114Dic61—22no—
115Dic61—41no—
116Dic61—42no—
117Dic61—41no—
118Dic61—42no—
119#2817—611nomaximal, Sylow
120C2×C61#53411yescharacteristic
121C2×C61#53611yescharacteristic
122C2×C61#53611yescharacteristic
123C2×C61#56312yes—
124C2×C61#56312yes—
125D61—42no—
126C2×C22⋊Q8—611no—
127C2×C22⋊Q8—611no—
128#400—611no—
129#400—612no—
130#400D6111yescharacteristic, complemented
131#397—612no—
132#397—612no—
133#395—611no—
134#395—612no—
135#395—611no—
136#381—611no—
137C61#281711yescharacteristic, complemented, Sylow
138C22×Q8—611no—
139C22×Q8—611no—
140C23×C4—611no—
141C22⋊Q8—1224no—
142C22⋊Q8—1224no—
143C2×C4⋊C4—611no—
144C2×C4⋊C4—612no—
145C2×C4⋊C4—611no—
146C2×C4⋊C4—612no—
147C2×C4⋊C4—612no—
148C2×C4⋊C4C2×D6111yescharacteristic
149C2×C4⋊C4C2×D6111yescharacteristic
150C2×C22⋊C4—611no—
151C2×C22⋊C4—611no—
152C2×C22⋊C4—612no—
153C2×C22⋊C4—612no—
154#95—612no—
155#95—611no—
156#95—612no—
157#95—612no—
158#95—612no—
159#95—612no—
160#95C2×D6111yescharacteristic
161#95C2×D6112yes—
162#95C2×D6112yes—
163C24—611no—
164C2×Q8—1222no—
165C2×Q8—1222no—
166C2×Q8—2442no—
167C2×Q8—2442no—
168C22×C4—611no—
169C22×C4—614no—
170C22×C4—612no—
171C22×C4—611no—
172C22×C4—611no—
173C22×C4—612no—
174C22×C4—2442no—
175C22×C4C22×D6112yes—
176C22×C4C22×D6112yes—
177C22×C4C22×D6111yescharacteristic
178C22×C4C22×D6111yescharacteristic
179C22×C4C22×D6111yescharacteristic
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—1222no—
183C4⋊C4—1224no—
184C4⋊C4—1222no—
185C4⋊C4—2442no—
186C4⋊C4—2442no—
187C22⋊C4—1222no—
188C22⋊C4—1224no—
189C22⋊C4—1222no—
190C22⋊C4—2442no—
191C23—612no—
192C23—1222no—
193C23—1222no—
194C23—1221no—
195C23—1221no—
196C23C23×D6111yescharacteristic
197Q8—2444no—
198Q8—2444no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—24no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—612no—
211C2×C4—1222no—
212C2×C4—1221no—
213C2×C4—1221no—
214C2×C4—1222no—
215C2×C4—1222no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1221no—
221C2×C4—1222no—
222C2×C4—1221no—
223C2×C4—2444no—
224C2×C4D4×D6112yes—
225C22—1222no—
226C22—1222no—
227C22—1222no—
228C22—2442no—
229C22—2442no—
230C22C2×D4×D6111yescharacteristic
231C22#1451982312yes—
232C22#1451982411yescharacteristic
233C22#1451982412yes—
234C22#1451982511yescharacteristic
235C4—22no—
236C4—42no—
237C4—41no—
238C4—42no—
239C4—41no—
240C4—1222no—
241C4—2442no—
242C4—2442no—
243C4—2441no—
244C4—2441no—
245C2—2442no—
246C2#1684032311yescharacteristic
247C2#1684033211yescharacteristic
248C2#1684033511yescharacteristic
249C2#1684051412yes—
250C2#1684051612yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#400C2
hypercenter#400D61
hypocenterC61#2817
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #400

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #16839704C2semidirect
4. #16839700C2semidirect
7. #16839683C2semidirect
8. #16839683C2semidirect
9. #16839682C2semidirect
11. C61×#400C2semidirect
130. #400D61semidirect
137. C61#2817semidirect